4.6$Features$of$Rational$Functions$

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4.6$Features$of$Rational$Functions

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A"Solidify!Understanding+Task! ! Part!I:!Identifying!features!of!rational!functions.! Using!prior!knowledge!of!other!functions!you!have!worked!with,!determine!the!features!of!each! rational!function!and!then!sketch!a!graph.!(features!include!intercepts,!domain,!asymptotes,!end! behavior*,!and!any!other!features!you!notice!about!each!rational!function).! !

! 1. ! ! =

!!! !!! !!!

2. ! ! =

!

!!! (!!!)(!!!)

!

3. !(!) =

(!!!)(!!!) !!!

!

! xGintercept(s):! !

! xGintercept(s):! !

yGintercept:!

yGintercept:!

yGintercept:!

Vertical!aysmptote(s):!

Vertical!aysmptote(s):!

Vertical!aysmptote(s):!

!

!

!

Proper!or!Improper:!

Proper!or!Improper:!

Proper!or!Improper:!

End!behavior! asymptotes*:!

End!behavior! asymptotes*:!

End!behavior! asymptotes*:!

!

!

Sketch!the!features!on! the!graph!below:!

Sketch!the!features!on! the!graph!below:!

Sketch!the!features!on! the!graph!below:!

!

!

!

!

!

!

!

Create!a!Sign!Line,!then! complete!graph!above:!

Create!a!Sign!Line,!then! complete!graph!above:!

Create!a!Sign!Line,!then! complete!graph!above:!

!

!

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!

! ! xGintercept(s):! !

!

!

!

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31 ! 4. Has!your!conjecture!about!the!end!behavior!of!rational!functions!changed?!Rewrite!your! conjecture!(including!any!modifications/changes!you!may!have!made):! ! ! 5. Complete!the!sentence:!The!domain!of!a!rational!function!is!all!real!numbers!except!! _________________________________________________________________________!.! ! Part!II:!Sketch!a!graph!of!each!rational!function.!Start!by!graphing!the!features!of!the!function!(same! features!from!Part!I),!then!‘fill!in’!the!rest!of!the!graph!using!a!sign!line!to!guide!you.! 6.!Asymptotes!and!sign!lines! 1 a.!f(x)!=! 2 !! ! x G9 !

!

!

!

!

!

!

G3 b.!f(x)!=!! 2 !! x G3x+2

!

2 1 c.!f(x)!=!! !! !!!!!d.!f(x)!=! 2!!!!! (xG1)2(x+2) x

!

(xG1)(x+2) c.!f(x)!=! 3 !!! (x +4x2+3x)

!

! 7.!Roots,!asymptotes,!and!sign!lines! Gx a.!f(x)!=!! 2 !! ! x G9 ! !

!

x+2 b.!f(x)!=!! 2 !! x G2x+1

!

!

! ! 3x2 d.!f(x)!=! 2 ! x G9

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V P! !

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